NUMERICAL-ANALYSIS OF FINITE-ELEMENT METHODS FOR MISCIBLE DISPLACEMENTS IN POROUS-MEDIA

Finite element methods are used to solve a coupled system of nonlinear partial differential equations, which models incompressible miscible displacement in porous media. Through a backward finite difference dis cretization in time, we define a sequentially implicit time-stepping a lgorithm that uncouples the system at each time-step. The Galerkin met hod is employed to approximate the pressure, and accurate velocity app roximations are calculated via a post-processing technique involving t he conservation of mass and Darcy's law. A stabilized finite element ( SUPG) method is applied to the convection-diffusion equation deliverin g stable and accurate solutions. Error estimates with quasi-optimal ra tes of convergence are derived under suitable regularity hypotheses. N umerical results are presented confirming the predicted rates of conve rgence for the post-processing technique and illustrating the performa nce of the proposed methodology when applied to miscible displacements with adverse mobility ratios. (C) 1998 John Wiley & Sons, Inc.